In a food processor, add flours, tarragon and 1/2 teaspoon salt - pulse to combine. Add butter, one piece at a time, pulsing once after each addition. Pour in oil and yogurt - pulse just until combined (it should be crumbly). Scoop the crumbles into a 9" tart pan lightly coated with nonstick spray - evenly press the dough over the bottom and up the sides to form a crust. Place into the oven and bake until the crust is just set, but has not taken on any color, about 15 minutes. Remove and place pan on a wire rack to cool

To prepare the filling

In a large skillet, heat oil over medium. Stir in onions - cook until tender, about 5 minutes. Stir in carrots and 1 tablespoon sherry - cook, stirring, for 2 minutes. Remove from the heat.

Add mustard onto the bottom of the crust and spread to form a thin layer. Scatter the top with the Cheddar. Cover the cheese evenly with the carrot and onion mixture.

In a medium bowl, whisk together eggs, milk, yogurt, tarragon and remaining 1 tablespoon sherry - season with salt and fresh ground black pepper. Set tart pan onto a baking sheet - pour the egg mixture over carrots and cheese. Place pan into the oven and bake until the center is set and the edges are golden brown, about 40 to 45 minutes. Remove and place pan on a wire rack to cool for at least 15 minutes before serving.